What will happen if you win the lottery for millions of dollars but live on SSI/SSDI?
SSI: No, the money is yours. However, once you win that lotto, you can't get SSI. Eventually, either the IRS or the bank will inform Social Security about the money, and you will have to pay every cent back. And SSI recipients are required to report these things.
SSDI: SSDI is insurance. If you crash your car, you get money to pay for it, even if you are rich. So winning the lotto is fine.